Intersection of Sets

Pronunciation: /ˌɪn tərˈsɛk ʃən/ ?

A series of images showing the intersection of A and B.
Figure 1: Intersection. Click on the image to see a representation of A ∩ B.

An intersection of two or more sets is a set containing the members that are in all of the sets. This is spoken, "Set C is the intersection of sets A and B." This is written, C = A ∩ B.

Properties of Intersection of Sets

PropertyMath StatementDescription
CommutativeA ∩ B = B ∩ AThe intersection of sets is commutative
Associative(D ∩ E) ∩ F = D ∩ (E ∩ F)The intersection of sets is associative
Distributive(D ∩ E) ∪ F = (D ∪ F) ∩ (E ∪ F)
(D ∪ E) ∩ F = (D ∩ F) ∪ (E ∩ F)
The intersection and union of sets are distributive
Table 1: Properties of the intersection of two sets.


  1. intersection. Encyclopedia Britannica. (Accessed: 2010-02-23).
  2. Von Neumann, John and Morgenstern, Oskar. Theory Of Games And Economic Behavior, 3rd edition, pg 63. Princeton University Press, 1953. (Accessed: 2010-02-23).
  3. Goldrei, D.C.. Classic Set Theory: For Guided Independent Study, pg 4. Chapman & Hall Mathematics, July 1, 1996.
  4. Gilbert, Jimmie; and Gilbert Linda. Elements of Modern Algebra, 6th edition, pg 4. Thomson, Brooks/Cole, 2005.

More Information

  • McAdams, David. Sets. Life is a Story Problem LLC. 2009-03-12.
  • McAdams, David. Set. All Math Words Encyclopedia. Life is a Story Problem LLC. 2009-12-15.

Printed Resources

Cite this article as:

Intersection of Sets. 2010-02-23. All Math Words Encyclopedia. Life is a Story Problem LLC.

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Revision History

2010-02-23: Added "References" (McAdams, David.)
2008-06-07: Corrected spelling (McAdams, David.)
2008-03-28: Added properties (McAdams, David.)
2007-08-01: Initial version (McAdams, David.)

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